Geometry and Topology: Q-deformation of stability conditions and quadratic differentials

Abstract: Categorically, we introduce Calabi-Yau-X categories, which are q-deformation of Haiden-Katzarkov-Kontsevich's topological Fukaya categories of flat surfaces. Their Calabi-Yau-N orbit categories are subcategories of derived Fukaya categories. Geometrically, we introduce and prove a q-deformation of Bridgeland-Smith theory, that realizes q-stability conditions on Calabi-Yau categories via multi-valued quadratic differentials on the corresponding surfaces. This is a joint work with Akishi Ikeda.